For the parametric equations: = 31e-4t and y = 32et %3D da

Q: nd a rectangular equation equivalent to the given pair of parametric equations. x= 7t-2, y=t; -3sts3

A:

Q: A baseball is hit towards the outfield, following the equations x(t)=51.5t and y(t)=−16t2+105t+4,…

A:

Q: For the parametric equations: x = 23e-4t and y 44e5t dx (?)

A:

Q: Graph the parametric graph and find the corresponding rectangular equation by eliminating the…

A: Given,

Q: Which of the following correctly gives the Cartesian form of the parametric equations x(t) = –7t – 2…

A:

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

A: We will find the time taken by the rocket to hits the ground as shown below

Q: For the parametric equations: a = 12e2t and y = 23e3t %3D da (i) dt dy (ii) dt dy (iii) dx ||

A:

Q: O Write the parametric equations x = 2t – °, y = 9 – 4t iven Cartesian form.

A: We have to write the given parametric equations into cartesian form

Q: A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop…

A:

Q: In the given equation as follows , sketch the curve represented by theparametric equations (indicate…

A:

Q: For the parametric equations: 22e2t and y = 47et

A: Derivative: - The derivative formula is one every of the foremost fundamental notions in calculus,…

Q: Find two different sets of parametric equations for the rectangular equation   y = 4/(x − 1)

A:

Q: Given the parametric equation. x = 2 cost y = 3sin t 0<t<2n

A: For (B), We need to find the curve whose parametric equation is given above.

Q: For the parametric equations: a = 30e2t and y = 47e3t %3D %3D da (i) dt dy (ii) dt dy (iii) da || ||

A:

Q: Find two different parametric equations for rectangular equation. y=-2x+4.

A: Two different parametric equations for the given rectangular equation y=-2x+4

Q: Sketch the curve represented by the parametric equations    x = et − 1,                    y = e3t…

A:

Q: ) Write the parametric equations x = x = 2t-t³, y = 3 - 2t in the given Cartesian form.

A:

Q: Given the parametric equations x = 3t2 and y = 4t3 , find (without eliminating t) dy а. and dx d²y…

A:

Q: The parametric equation for the y-axis is:

A:

Q: Find the rectangular equation for given parametric equations x= 3t      y=t+3

A:

Q: Find two different sets of parametric equations for the rectangular equation y = x2 + 4.

A: To find the set of parametric equations

Q: Eliminate the parameter in the parametric equations a(t) = –8t – 9 and y(t) = –32t + 9 to write a…

A: Given parametric equations, x(t)=-8t-9 y(t)=-32t+9

Q: For the parametric equations: a = 12e and y = 29e3t dr (i) dt dy (ii) dt dy (iii) dr || ||

A:

Q: By eliminating the parameter t, sketch the following parametric equations x=5sint and y=6cost..

A:

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

A:

Q: Find two different sets of parametric equations for the rectangular equation y = 4x - 3.

A:

Q: Write the parametric equations in rectangular form. y= 2f + 6 x = 5t – 8 -

A: Given,           The parametric equations are             y=2t2+6             x=5t-8

Q: -4t For the parametric equations: x = 48e and y = 37e5t

A:

Q: find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

A: To find the parametric equation of the given curve (x+9)2+(y-4)2=49 Given equation is in the form of…

Q: Find the parametric equation from the given rectangular equation a.    y = 3x-3   b.   y= (x-3)2 /2

A:

Q: Write the parametric equations = Vi, y = 2 – t x in Cartesian form. y = with x > 0

A:

Q: The motion of a particle in space is defined by the parametric equation x(t)=-t2+3t+1,in meter and…

A: To find the position of the particle, use the formula, r→(t)=x(t),y(t), where x(t) is the…

Q: Find two different sets of parametric equations for the rectangular equation: y = 2x - 5.

A: Given, y=2x-5

Q: Graph the following set of parametric equations and show the orientation of the curve: x=-3t +1 17.…

A:

Q: x = 1 + 4t,    y = 3 − t2

A: Here we extract t from the 1st equation then put this into second equation.

Q: What is the rectangular equation of the curve fro the parametric equation below? x=3t+2,…

A: Consider the parametric equation, x=3t+2y=t+40≤t≤4

Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x= -2 t+6 y=…

A:

Q: Find the equation for the following parametric equation in rectangular coordinates. x = 2t + 1 y =…

A: The solution is :

Q: Find the Cartesian equation and graph the curve whose parametric equations are: X=-2+3t Y=1-2t

A: The given parametric equations are X=-2+3t and Y=1-2t To find the cartesian equation of the given…

Q: Sketch the curve represented by the parametric equations x = 1 + 8t,                 y = 3 − 4t…

A: x=1+8t,  y=3-4t When t=0, x=1+80, y=3-40⇒x=1, y=3 When t=1, x=1+81, y=3-41⇒x=9, y=-1 Now the graph…

Q: Write the parametric equations x = 4t – t³, y=2 – 3t in the given Cartesian form.

A:

Q: For the parametric equations: x = 9e-4t and y = 8e5t %3D dx dt dy (ii) dt %3D dy (ii) dx (write the…

A:

Q: find the parametric equation for each of the following a.) for the line of slope 2 passing through…

A: a) Firstly, we will find the equation of line of slope 2 passing through the point (-2,4) by using…

Q: For the parametric equations: a = 16et and y 18e %3D da (i) dt 32*e^(2t) %3D dy (ii) dt 54*e^(3t)…

A:

Q: Given the parametric equations I = dy 9t2 and y = 4t, then %3D 2t Windows bD

A:

Q: Write the parametric equations x = 5t – t, y= 2 – 5t in the given Cartesian form. x =

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.